Question

An important news announcement is transmitted by radio waves to people who are 82 km away, sitting next to their radios, and by sounds waves to people sitting across the newsroom, 4.7 m from the newscaster. Take the speed of sound in air to be 340 m/s.

What is the difference in time that the message is received?
Answer in units of ms.

Answer 1

13.5 ms

Step-by-step explanation:

The sound wave travels with uniform motion in both cases, so the time taken to cover a distance d is given by:

`t=(d)/(v)`

where

d is the distance to cover

v = 340 m/s is the speed of sound in air

So for the people across the newsroom,

d = 4.7 m

So the time taken is

`t=(4.7)/(340)=0.0138 s = 13.8 ms`

The radio waves instead travels with uniform motion at the speed of light:

`c=3.0\cdot 10^8 m/s`

So the time taken for them is

`t=(d)/(c)`

where

d = 82 km = 82,000 m

is the distance of the people who are 82 km away. Substituting,

`t=(82,000)/(3.0\cdot 10^8)=0.27\cdot 10^(-3) s = 0.27 ms`

Therefore, the difference in time is

`\Delta t = 13.8 ms - 0.27 ms = 13.5 ms`